This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. Numerical trial results on this page are restricted to the results posted in the ClinicalTrials.gov record; calculations added by Clinical Biostats are labelled as such.
1. Trial at a Glance
This page covers the registry results for Combination Chemotherapy in Treating Women Who Have Undergone Surgery for Node-Positive Breast Cancer (NCT00093795), a randomized phase 3 study. The primary outcome is Disease-free Survival: Any Recurrence, Contralateral Breast Cancer, Second Primary Cancer, Death From Any Cause Prior to Recurrence or Second Primary Cancer.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT00093795 |
| Phase | Phase 3 |
| Condition | Breast Cancer |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | None (open label) |
| Enrollment | 4894 |
| Arms in the primary outcome | 3 |
| Lead sponsor | NSABP Foundation Inc |
| Results posted | Yes |
2. Clinical Question
Population
Women with node-positive breast cancer who had undergone surgery. The registry record describes a total enrollment of 4894 participants.
Intervention
One randomized regimen was TAC X 6: doxorubicin, cyclophosphamide and docetaxel.
Comparator
The other regimens were AC X 4 then P X 4, using doxorubicin, cyclophosphamide and paclitaxel, and AC X 4 then PG X 4, adding gemcitabine to paclitaxel after doxorubicin and cyclophosphamide.
Primary question
How did the three regimens compare on the percentage of patients alive and cancer-free at five years, using a disease-free survival definition that also counts specified recurrence, second-cancer and death events?
The study addressed an adjuvant treatment question: after surgery, how did outcomes compare across three combination chemotherapy strategies for women with node-positive breast cancer? The primary endpoint was not limited to recurrence of the original cancer. Its event definition also included contralateral breast cancer, a second primary cancer, and death from any cause before recurrence or a second primary cancer.
The registry describes a randomized, parallel-group, phase III trial without masking. Participants were assigned to one of the three regimens; the primary outcome was reported as a percentage at five years. This design supports comparison among the assigned groups, while the posted outcome summaries alone do not describe the details of treatment delivery, follow-up procedures, or the analysis used by the investigators.
The posted figures describe disease-free survival within each group and unadjusted pairwise contrasts against the TAC group. They do not establish that any regimen is superior or equivalent. The estimates and their uncertainty are the basis for interpreting what the registry record shows, while limitations in reported analysis details and follow-up should remain part of that interpretation.
3. Trial Design
This was a phase III randomized parallel-group trial with no masking reported. It enrolled 4894 participants and is marked completed in the registry record. The study population was women with node-positive breast cancer who had undergone surgery. The trial compared three adjuvant chemotherapy regimens.
Group 1 received TAC X 6, described as doxorubicin, cyclophosphamide and docetaxel. Group 2 received AC X 4 then P X 4, described as doxorubicin, cyclophosphamide and paclitaxel. Group 3 received AC X 4 then PG X 4, described as doxorubicin, cyclophosphamide, paclitaxel and gemcitabine. The record gives these regimen descriptions but does not report further dosing or administration details in the information summarized for the outcomes.
The primary endpoint was disease-free survival at five years, expressed as the percentage of patients meeting the registry's alive-and-cancer-free description. The endpoint's event definition was broader than recurrence alone: it included contralateral breast cancer, a second primary cancer, and death from any cause before recurrence or a second primary cancer. The posted group sizes for the primary outcome were 1610 for TAC, 1618 for AC then paclitaxel, and 1613 for AC then paclitaxel plus gemcitabine.
Follow-up data were unavailable for 20 participants in Arm 1, 16 in Arm 2 and 17 in Arm 3, according to the primary outcome description. The registry record does not report the trial's original sample-size assumptions, the planned primary analysis, analysis-population definitions, or interim-monitoring procedures. It also lists no reported formal analyses for the outcomes discussed in the record. The posted estimates can therefore be described, but the analysis details underlying the sponsor's conclusions are not available in the registry record.
4. Participant Flow and Accounting
The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.
Overall Study
| Stage | Group 1: TAC X 6 | Group 2: AC X 4 Then P X 4 | Group 3: AC X 4 Then PG X 4 |
|---|---|---|---|
| STARTED | 1630 | 1634 | 1630 |
| COMPLETED | 1610 | 1618 | 1613 |
| NOT COMPLETED | 20 | 16 | 17 |
Reasons for not completing this period:
| Reason | Group 1: TAC X 6 | Group 2: AC X 4 Then P X 4 | Group 3: AC X 4 Then PG X 4 |
|---|---|---|---|
| No follow up data | 20 | 16 | 17 |
Analysis population for the primary outcome, as defined in the registry: For Arm 1 there is no follow-up data for 20 participants; for Arm 2 there is no follow-up data for 16 participants; and for Arm 3 there is no follow-up data for 17 participants.
5. Baseline Characteristics
The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.
| Characteristic | Unit | TAC X 6 | AC X 4 Then P X 4 | AC X 4 Then PG X 4 | Total |
|---|---|---|---|---|---|
| Participants analysed | 1623 | 1623 | 1621 | 4867 | |
| Age, Continuous | years | 51 (SD 9.5) | 51 (SD 9.5) | 51 (SD 9.4) | 51 (SD 9.5) |
| Sex: Female, Male: Female | Participants | 1623 | 1623 | 1621 | 4867 |
| Sex: Female, Male: Male | Participants | 0 | 0 | 0 | 0 |
6. Primary Endpoint
The registry lists the primary outcome as Disease-free Survival: Any Recurrence, Contralateral Breast Cancer, Second Primary Cancer, Death From Any Cause Prior to Recurrence or Second Primary Cancer, measured over 5 years.
| Element | Registry entry |
|---|---|
| Result type | Number |
| Measure of spread | 95% Confidence Interval |
| Unit | percentage of patients |
| Endpoint classification | Binary Endpoint |
The primary endpoint is five-year disease-free survival, reported as a percentage of patients. The registry describes this as the percentage alive and cancer-free. Its event definition includes any recurrence, cancer in the contralateral breast, a second primary cancer, or death from any cause before recurrence or a second primary cancer. This composite therefore captures more than return of the original cancer, and an event can occur through several different pathways.
A composite endpoint can summarize several clinically relevant outcomes in one measure and increase the number of events contributing to the overall assessment. Its interpretation depends on which components are included: a group difference in the composite would not by itself show which component contributed to that difference. Component-specific results and their analysis are not reported for the primary endpoint in the registry record.
The five-year percentage gives a time-specific view of the outcome rather than a complete account of how events unfolded over follow-up. A percentage at a stated time can be readily interpreted as a proportion, while it does not convey the timing of individual events or the shape of outcome patterns between measured times. The registry reports 95% confidence intervals around the group percentages. Those intervals express uncertainty in the estimates, not the range of individual participant outcomes.
The outcome description notes participants without follow-up data in each arm. Missing follow-up can affect estimates if those participants' outcomes differ from those observed, but the registry record does not describe how missing data were handled. That absence limits assessment of how the reported endpoint percentages relate to all randomized participants.
7. Results Posted in the Registry
- Group 2: AC X 4 Then P X 4: 82.2% (1330/1618) versus 80.1% (1290/1610) on control; risk difference 2.1 percentage points (95% CI -0.6 to 4.8), risk ratio 1.03 (0.99–1.06); unadjusted two-proportion z-test p = 0.131.
- Group 3: AC X 4 Then PG X 4: 80.6% (1300/1613) versus 80.1% (1290/1610) on control; risk difference 0.5 percentage points (95% CI -2.3 to 3.2), risk ratio 1.01 (0.97–1.04); unadjusted two-proportion z-test p = 0.736.
Risk difference: Group 2: AC X 4 Then P X 4
95% CI: -0.6 to 4.8 percentage points
Recalculated from the posted summary statistics
8. Secondary Efficacy Endpoints
The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.
| Secondary outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Recurrence-free Interval: Time to First Local, Regional, or Distant Recurrence | Binary Endpoint | Risk difference | +1.1 pts (-1.3 to 3.5) | 15,256 per arm |
| Distant Recurrence-free Interval: the Time to Distant Disease Recurrence Only | Binary Endpoint | Risk difference | +0.8 pts (-1.5 to 3.1) | 27,216 per arm |
| Toxicity | Binary Endpoint | Risk difference | +4.8 pts (2.3 to 7.2) | 866 per arm |
Recurrence-free Interval: Time to First Local, Regional, or Distant Recurrence
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Group 2: AC X 4 Then P X 4: 86.2% (1395/1618) versus 85.1% (1370/1610) on control; risk difference 1.1 percentage points (95% CI -1.3 to 3.5), risk ratio 1.01 (0.99–1.04); unadjusted two-proportion z-test p = 0.362.
- Group 3: AC X 4 Then PG X 4: 84.8% (1368/1613) versus 85.1% (1370/1610) on control; risk difference -0.3 percentage points (95% CI -2.8 to 2.2), risk ratio 1.00 (0.97–1.03); unadjusted two-proportion z-test p = 0.823.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Group 2: AC X 4 Then P X 4 and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Group 3: AC X 4 Then PG X 4 and the control. The interval gives the range of effects that remain compatible with the data.
Distant Recurrence-free Interval: the Time to Distant Disease Recurrence Only
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Group 2: AC X 4 Then P X 4: 87.4% (1414/1618) versus 86.6% (1394/1610) on control; risk difference 0.8 percentage points (95% CI -1.5 to 3.1), risk ratio 1.01 (0.98–1.04); unadjusted two-proportion z-test p = 0.495.
- Group 3: AC X 4 Then PG X 4: 86.6% (1397/1613) versus 86.6% (1394/1610) on control; risk difference 0.0 percentage points (95% CI -2.3 to 2.4), risk ratio 1.00 (0.97–1.03); unadjusted two-proportion z-test p = 0.983.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Group 2: AC X 4 Then P X 4 and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Group 3: AC X 4 Then PG X 4 and the control. The interval gives the range of effects that remain compatible with the data.
Toxicity
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Group 2: AC X 4 Then P X 4: 87.5% (1420/1623) versus 82.7% (1329/1607) on control; risk difference 4.8 percentage points (95% CI 2.3 to 7.2), risk ratio 1.06 (1.03–1.09); unadjusted two-proportion z-test p = <0.001.
- Group 3: AC X 4 Then PG X 4: 88.4% (1425/1612) versus 82.7% (1329/1607) on control; risk difference 5.7 percentage points (95% CI 3.3 to 8.1), risk ratio 1.07 (1.04–1.10); unadjusted two-proportion z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the proportion with the event is statistically higher for Group 2: AC X 4 Then P X 4 than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
- The 95% confidence interval excludes no difference, so the proportion with the event is statistically higher for Group 3: AC X 4 Then PG X 4 than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The secondary outcomes broaden the assessment beyond the primary composite. They include recurrence-free interval, distant recurrence-free interval and toxicity, as well as overall survival in the outcome list. The registry record posts results for the recurrence intervals and toxicity, but formal analyses are not reported. A consistent high-level pattern is that the recurrence outcomes do not resolve clear between-group differences in the posted unadjusted comparisons, while the toxicity summaries point in a different direction from the recurrence summaries.
This pattern gives context to, but does not replace, the primary result. The recurrence outcomes are related to disease-free survival because recurrence contributes to the primary endpoint, but their definitions differ: the primary measure also includes contralateral breast cancer, second primary cancer and death under its stated rules. Distant recurrence-free interval focuses on distant disease recurrence, while recurrence-free interval concerns first local, regional or distant recurrence. Similarity across measures can be reassuring descriptively, but does not establish that all endpoint components behave alike.
The toxicity outcome is a distinct dimension of the comparison and should not be folded into disease-free survival. It represents an outcome assessed at a different timeframe and with a different event definition. The overall pattern therefore involves more than a single benefit-like dimension; outcome domains may point in different directions and need to be considered separately.
Unadjusted secondary comparisons carry less weight because examining multiple outcomes and multiple pairwise contrasts increases the chance of finding apparently notable results by chance. No multiplicity procedure is reported in the registry record. These secondary estimates are consequently best treated as descriptive evidence requiring caution, rather than as a definitive ranking of regimens or an independent confirmation of the primary result. Overall survival is listed as a secondary outcome, but its results are not reported in the registry record.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Overall Survival
- Recurrence-free Interval: Time to First Local, Regional, or Distant Recurrence
- Distant Recurrence-free Interval: the Time to Distant Disease Recurrence Only
- Toxicity
9. Statistical Interpretation
At five years, the posted disease-free survival estimate was 80.1% for TAC, 82.2% for AC then paclitaxel, and 80.6% for AC then paclitaxel plus gemcitabine. Each estimate is accompanied by a 95% confidence interval: 78.0% to 82.0%, 80.2% to 84.0%, and 78.5% to 82.5%, respectively. These are arm-level summaries. They do not by themselves quantify the uncertainty in a between-group difference.
The unadjusted recalculated risk difference for AC then paclitaxel compared with TAC was 0.021, with a 95% confidence interval from -0.006 to 0.048 and an unadjusted p-value of 0.131. For AC then paclitaxel plus gemcitabine compared with TAC, the risk difference was 0.005, with a 95% confidence interval from -0.023 to 0.032 and an unadjusted p-value of 0.736. Both intervals include zero, so the estimates are compatible with no difference as well as with differences in either direction. They also allow for a range of possible magnitudes; they are not proof that the groups are identical.
The arm-level percentages are close, but closeness alone does not establish equivalence or noninferiority. Those conclusions require an appropriate design, a prespecified margin and an analysis addressing that margin. Such information is not reported in the registry record. Likewise, a non-significant unadjusted p-value does not demonstrate that a difference is absent. It indicates that the observed contrast, under the assumptions of the calculation, does not provide strong evidence against a zero difference at conventional thresholds.
The two comparisons share the same TAC reference group. Their estimates should not be treated as independent replications, and the registry record does not report a multiplicity adjustment for the pairwise comparisons. The risk differences and p-values are unadjusted recalculations from posted summary statistics, rather than reported sponsor analyses. The sponsor's own analysis takes precedence if a discrepancy is present; the record indicates no discrepancy for these calculations.
The evidence is therefore best read descriptively: the posted five-year percentages fall in a relatively narrow range, while the comparison intervals remain broad enough to include no difference and some effects in either direction. The data do not answer every question about longer-term outcomes, individual endpoint components or treatment trade-offs. The registry also lists secondary outcomes, but formal analyses for those outcomes are not reported in the registry record. Statistical interpretation should stay within the information reported and should not turn these estimates into a claim about whether a regimen works.
10. Statistical Methods Explained
What does a group percentage describe?
The primary outcome is a binary event measure summarized as a percentage of patients at five years. Each group estimate describes the proportion meeting the registry's disease-free survival definition. A percentage is an absolute summary for that group; it is not a comparison by itself. To compare groups, one can examine an absolute difference in their percentages, a relative measure, or a model-based estimate. The posted recalculated pairwise statistic is a risk difference, which expresses the contrast on the percentage-proportion scale.
For the primary outcome, the reference group is TAC. The displayed pairwise estimates compare each of the other groups with TAC. The estimate's sign indicates the direction under the stated comparison ordering, while the confidence interval indicates the range of differences compatible with the data and calculation assumptions. An interval spanning zero includes no difference. This does not prove equality: meaningful positive or negative differences may also lie within the interval.
What does a confidence interval add?
A confidence interval conveys precision around an estimate. In general, a 95% confidence interval is generated by a procedure that, under its assumptions and repeated use, would cover the target quantity in 95% of such intervals. It is not a statement that there is a 95% probability that this particular fixed interval contains the true value. For a group percentage, the interval concerns that group's outcome proportion; for a risk difference, it concerns the contrast between groups.
Intervals are more informative than a point estimate alone because they show how much uncertainty remains. A narrow interval means greater precision for the specified estimate under the method used; a wide interval means less precision. Precision is not the same as freedom from bias. A narrow interval cannot correct a poorly defined endpoint, missing-data problems, or limitations in the analysis population.
How should p-values be read?
A p-value describes how incompatible the observed data are with a specified null model, assuming that model and the calculation assumptions are correct. It is not the probability that the null hypothesis is true, nor is it a measure of clinical importance. The posted primary comparisons have unadjusted p-values of 0.131 and 0.736. Their corresponding confidence intervals include zero, consistent with the absence of a clear distinction from zero in these unadjusted summaries.
These values come from unadjusted recalculations based on the posted summary statistics. They should not be confused with a complete investigator analysis, which could include adjustment, stratification, censoring rules, covariates or other methods. Those methods are not reported in the registry record. The record also lists no reported formal analyses, so there is no described sponsor analysis to substitute for these recalculated contrasts.
Why do the endpoint and design matter?
The primary measure is a composite: several types of recurrence, second primary cancer and death contribute to the endpoint. This provides a broad disease-free survival summary, but a difference in the composite would not identify which component accounts for it. A single percentage at five years also omits event timing and does not show whether risk changes over time. The registry separately names recurrence-free and distant recurrence-free outcomes, but their analysis details are not reported in the record.
Randomization is intended to support fair comparisons by assigning participants to groups, rather than allowing treatment choice alone to determine group membership. The registry identifies randomized allocation and a parallel model, but does not report the randomization method, any stratification factors, concealment procedures or analysis-population rules. No masking was reported. These registry entries describe the stated design without resolving all possible sources of bias or explaining how the analysis handled deviations from assigned treatment.
What is the role of over-dispersion?
Over-dispersion is a general concern when observed variation is greater than a statistical model assumes. In binary outcomes, dependence among observations or variation in underlying risks can make a simple model understate uncertainty if it assumes independent observations with one common risk. Appropriate methods may account for clustering or heterogeneity when the design and data call for them. The registry record does not report evidence of over-dispersion, clustering, or methods used to address either, so no trial-specific conclusion about these issues can be drawn.
The posted confidence intervals and recalculated comparisons should consequently be read as summaries based on the methods used to produce them, not as a substitute for a complete statistical analysis plan. The registry record does not describe model diagnostics, covariate adjustment, censoring procedures, endpoint adjudication, or sensitivity analyses. Those omissions matter when assessing whether the estimates answer the intended question under the study's actual data structure.
11. Confidence Intervals and Precision
The primary arm estimates are 80.1% for TAC, 82.2% for AC then paclitaxel, and 80.6% for AC then paclitaxel plus gemcitabine. Their 95% confidence intervals are 78.0% to 82.0%, 80.2% to 84.0%, and 78.5% to 82.5%. The intervals overlap substantially. Overlap between arm-level intervals is not itself a formal test of the difference; the pairwise risk-difference intervals are the more direct summaries for that comparison.
For the comparison of AC then paclitaxel with TAC, the estimated risk difference is 0.021 and its 95% confidence interval ranges from -0.006 to 0.048. For AC then paclitaxel plus gemcitabine compared with TAC, the estimate is 0.005 and its interval ranges from -0.023 to 0.032. Each interval includes zero and permits effects on either side of zero. The intervals therefore do not precisely locate the contrast as a single value; they show uncertainty around the point estimates.
Confidence intervals are about precision under a statistical procedure, not certainty about clinical importance. The registry record does not report a threshold for a clinically important difference, nor an equivalence or noninferiority margin. Consequently, these intervals cannot be judged against a prespecified margin based on the record. They also do not address bias from missing follow-up or unreported analysis choices.
The primary outcome description records missing follow-up for 20 participants in Arm 1, 16 in Arm 2 and 17 in Arm 3. The record does not state how those participants were handled in the estimates or provide a missing-data sensitivity analysis. Without that information, confidence intervals alone cannot convey all sources of uncertainty in the result.
12. Planning a Similar Trial: Sample Size
This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.
| Effect to detect | Participants per arm, 80% power | Participants per arm, 90% power |
|---|---|---|
| 100% of the observed effect | 5,568 | 7,453 |
| 75% of the observed effect | 10,004 | 13,391 |
| 50% of the observed effect | 22,742 | 30,444 |
The planning figures are illustrations of sample sizes associated with detecting different fractions of the observed effect, not a reconstruction of the trial's original design. The calculation assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, a normal approximation, and an effect to detect set to the stated fraction of the observed effect. The trial's own original sample-size assumptions are not reported in the registry record.
For ordinary binary outcomes, the estimates are participants per arm. For time-to-event outcomes, the figures are total events, using the Schoenfeld approach. The unit matters: a total-event target is not a participant count, because participants may have different follow-up and not all will experience an event. The primary disease-free survival calculation is an ordinary binary outcome and its planning figures are per arm.
The 80% power column gives the estimated number needed under the stated assumptions for an 80% chance of detecting the specified effect if that effect were true. The 90% power column gives the corresponding target for a 90% chance. Power is a property of a planned study under assumed conditions, not a probability that a particular result is correct. These planning figures are not observed power.
Each row changes the assumed effect to detect: the full observed effect, 75% of it, or 50% of it. Smaller effects are harder to distinguish from random variation, so they require more participants or events for the same power and significance level. When an observed contrast is small, its extrapolated planning target can become very large. Such estimates are sensitive to the observed effect used as their starting point, and should not be read as a recommendation for a future trial without a separate design justification.
These calculations do not describe the actual enrollment target or the reasoning behind it. They also do not account, in the assumptions listed, for details such as missing follow-up, unequal allocation, interim monitoring, adjustment for multiple comparisons or a different analysis model. Those original design features are not reported in the registry record.
13. How the Sample Size Is Derived
Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z1−α/2 = 1.960) and the desired power (z1−β = 0.842 for 80% and 1.282 for 90%).
Formula
n is the number of participants in each arm, p0 and p1 are the control and treatment proportions, and p̄ is their average.
Worked calculation for this trial
- Control proportion p0 = 0.801; treatment proportion p1 = 0.822; average p̄ = 0.812.
- First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.5530 = 1.0838.
- Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.5528 = 0.4652.
- n = (1.0838 + 0.4652)2 / (0.0208)2 = 5,567.6, rounded up to 5,568 participants per arm for 80% power.
The smaller-effect rows in the table above repeat the same calculation with the effect multiplied by 0.75 and 0.5 (for ratios, applied to the logarithm of the ratio).
R code
alpha <- 0.05
z_a <- qnorm(1 - alpha / 2) # two-sided
p0 <- 0.801242236024845 # control proportion
p1 <- 0.822002472187886 # treatment proportion
n_per_arm <- function(power, frac = 1) {
q1 <- p0 + (p1 - p0) * frac # smaller effect = fraction of the observed difference
pbar <- (p0 + q1) / 2
z_b <- qnorm(power)
ceiling(round((z_a * sqrt(2 * pbar * (1 - pbar)) + z_b * sqrt(p0 * (1 - p0) + q1 * (1 - q1)))^2 / (q1 - p0)^2, 6))
}
for (f in c(1, 0.75, 0.5))
cat(sprintf("%3.0f%% of observed effect: n per arm = %s (80%% power), %s (90%% power)\n", 100 * f,
format(n_per_arm(0.80, f), big.mark = ","), format(n_per_arm(0.90, f), big.mark = ",")))
# Check against R's built-in function (unrounded n per arm)
cat("power.prop.test:", round(power.prop.test(p1 = p0, p2 = p1, power = 0.80)$n, 1), "\n")
# Simulation: how often does the z-test reject at the 80%-power sample size?
set.seed(93795)
n <- n_per_arm(0.80)
reps <- 20000
x0 <- rbinom(reps, n, p0); x1 <- rbinom(reps, n, p1)
ph <- (x0 + x1) / (2 * n)
z <- ((x1 - x0) / n) / sqrt(ph * (1 - ph) * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE), reps))
Output from running the code
100% of observed effect: n per arm = 5,568 (80% power), 7,453 (90% power)
75% of observed effect: n per arm = 10,004 (80% power), 13,391 (90% power)
50% of observed effect: n per arm = 22,742 (80% power), 30,444 (90% power)
power.prop.test: 5567.6
Simulated power at n = 5,568 per arm: 0.804 (20000 replicates)
The simulation draws many pairs of event counts at the planned sample size and counts how often the two-proportion z-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.
14. Multiplicity, Missing Data and Analysis Populations
Several choices that affect interpretation are not reported in the registry record. The record does not describe a statistical analysis plan, analysis populations, methods for handling missing data, interim analyses, stopping rules, or adjustment for multiple comparisons. It also does not explain whether any covariates or stratification factors were included in the original analysis. The absence of these details prevents a full assessment of how the posted estimates were generated and which analyses were prespecified.
Multiplicity is relevant because the study compares three groups and reports several outcomes. Each additional contrast or outcome creates another opportunity for an apparently unusual result under a null effect. A multiplicity adjustment can control the overall false-positive risk across a family of tests, but no such adjustment is described in the registry record. The pairwise p-values discussed for the primary outcome are unadjusted recalculations; the secondary outcome comparisons are also unadjusted. Their interpretation should account for the number of questions considered, rather than treating each p-value as if it were the only test.
The primary endpoint description notes no follow-up data for 20 participants in Arm 1, 16 in Arm 2 and 17 in Arm 3. This is important because the estimate can depend on how participants without observed follow-up are handled. The record does not state whether they were censored, excluded, treated as events, or addressed through another method. These are possibilities in general, not claims about what happened in this trial. No sensitivity analyses for missing data are reported.
Analysis populations also matter. An intention-to-treat analysis generally retains participants in their randomized groups, whereas per-protocol or as-treated analyses can answer different questions and may introduce other biases. The registry record does not identify which populations underlie the posted outcome estimates, nor does it describe adherence, crossover or exclusions. No assumptions about these aspects can therefore be made. These gaps do not invalidate the posted summaries, but they limit how completely they can be evaluated.
15. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| TAC X 6 | 277 | 1601 | 17.3% |
| AC X 4 Then P X 4 | 158 | 1612 | 9.8% |
| AC X 4 Then PG X 4 | 187 | 1604 | 11.7% |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 5% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| TAC X 6 | 1231 of 1601 |
| AC X 4 Then P X 4 | 1322 of 1612 |
| AC X 4 Then PG X 4 | 1323 of 1604 |
Most frequent serious adverse event terms
| Event term | Organ system | TAC X 6 | AC X 4 Then P X 4 | AC X 4 Then PG X 4 |
|---|---|---|---|---|
| Febrile neutropenia | Blood and lymphatic system disorders | 40 of 1601 | 45 of 1612 | 132 of 1604 |
| Fatigue | General disorders | 43 of 1601 | 37 of 1612 | 27 of 1604 |
| Dehydration | Metabolism and nutrition disorders | 22 of 1601 | 42 of 1612 | 23 of 1604 |
| Nausea | Gastrointestinal disorders | 26 of 1601 | 35 of 1612 | 18 of 1604 |
| Diarrhea | Gastrointestinal disorders | 9 of 1601 | 17 of 1612 | 47 of 1604 |
| Vomiting | Gastrointestinal disorders | 22 of 1601 | 14 of 1612 | 23 of 1604 |
| Dyspnea | Respiratory, thoracic and mediastinal disorders | 19 of 1601 | 23 of 1612 | 14 of 1604 |
| Abdominal pain | Gastrointestinal disorders | 21 of 1601 | 8 of 1612 | 13 of 1604 |
| Myalgia | Musculoskeletal and connective tissue disorders | 15 of 1601 | 9 of 1612 | 10 of 1604 |
| Pneumonitis | Respiratory, thoracic and mediastinal disorders | 10 of 1601 | 16 of 1612 | 6 of 1604 |
Most frequent non-serious adverse event terms
| Event term | Organ system | TAC X 6 | AC X 4 Then P X 4 | AC X 4 Then PG X 4 |
|---|---|---|---|---|
| Fatigue | General disorders | 805 of 1601 | 784 of 1612 | 774 of 1604 |
| Nausea | Gastrointestinal disorders | 510 of 1601 | 504 of 1612 | 497 of 1604 |
| Myalgia | Musculoskeletal and connective tissue disorders | 256 of 1601 | 536 of 1612 | 512 of 1604 |
| Bone pain | Musculoskeletal and connective tissue disorders | 267 of 1601 | 484 of 1612 | 446 of 1604 |
| Peripheral sensory neuropathy | Nervous system disorders | 167 of 1601 | 484 of 1612 | 428 of 1604 |
| Vomiting | Gastrointestinal disorders | 284 of 1601 | 245 of 1612 | 306 of 1604 |
| Diarrhea | Gastrointestinal disorders | 325 of 1601 | 159 of 1612 | 185 of 1604 |
| Constipation | Gastrointestinal disorders | 154 of 1601 | 204 of 1612 | 184 of 1604 |
| Mucositis oral | Gastrointestinal disorders | 173 of 1601 | 157 of 1612 | 201 of 1604 |
| Headache | Nervous system disorders | 142 of 1601 | 182 of 1612 | 188 of 1604 |
Serious events with the highest arm-level rate: febrile neutropenia (8.2%), diarrhea (2.9%), fatigue (2.7%), dehydration (2.6%), nausea (2.2%).
The registry lists serious adverse event counts among participants at risk: 277 of 1601 for TAC, 158 of 1612 for AC then paclitaxel, and 187 of 1604 for AC then paclitaxel plus gemcitabine. It also lists other adverse event counts: 1231 of 1601, 1322 of 1612, and 1323 of 1604, respectively. These counts are separate from the primary disease-free survival outcome and should be interpreted according to the safety definitions used in the record.
Listed serious adverse event terms include febrile neutropenia at 8.2%, diarrhea at 2.9%, fatigue at 2.7%, dehydration at 2.6%, nausea at 2.2%, and vomiting at 1.4%. The record does not specify the group-specific percentages for these terms in the information summarized. Death counts are not reported in the registry record. The toxicity outcome is described at 30 days after the last dose of study therapy, about 7 months after study entry; this timeframe differs from the five-year primary endpoint.
These summaries describe reported events, not a complete causal assessment. They do not establish why an event occurred or indicate how its severity, duration or management differed by group. The adverse-event figures should be considered alongside the distinct efficacy outcomes without treating one as a substitute for the other.
16. What the Result Does, and Does Not, Mean
The posted primary result shows five-year disease-free survival percentages of 80.1% for TAC, 82.2% for AC then paclitaxel, and 80.6% for AC then paclitaxel plus gemcitabine. The unadjusted pairwise risk-difference intervals include zero for both comparisons with TAC. The record therefore does not provide a precise basis for claiming a clear difference in the primary outcome between either sequential regimen and TAC from these recalculated summaries.
That interpretation is not the same as saying that the regimens are equivalent, that no difference exists, or that any regimen is effective or ineffective. Evidence of equivalence or noninferiority requires a prespecified margin and an appropriate analysis; the margin and such an analysis are not reported in the registry record. Conversely, an interval including zero does not rule out all potentially relevant differences. It indicates that the posted estimate remains uncertain over a range that includes no difference.
The primary endpoint is a composite with several event types, and the registry does not report component-specific primary results. The five-year percentages also do not describe the timing of events or longer-term patterns. Secondary outcomes add context, but their formal analyses are not reported and the number of comparisons raises multiplicity concerns. Toxicity represents a separate outcome domain, with a different measurement timeframe.
Missing follow-up is noted for participants in all three arms, but the registry record does not explain its handling. Analysis-population definitions, the primary analysis method, interim monitoring, and the original sample-size justification are also not reported. Those details could affect how confidently the results are interpreted. The most defensible conclusion is therefore descriptive: the observed primary percentages are in a similar range, and the unadjusted pairwise intervals do not isolate a difference from zero. The posted information does not support a broader claim about comparative clinical merit.
17. Why This Trial Matters Statistically
This trial poses a statistically important comparison among three active, multi-drug regimens in a randomized parallel design. The question is not simply whether an outcome occurred, but how the groups compare under a composite five-year disease-free survival definition. Making the endpoint components explicit matters because recurrence, contralateral breast cancer, second primary cancer and death are distinct events that contribute to one summary.
The results also illustrate why point estimates and uncertainty should be read together. The group percentages offer an accessible summary, while the pairwise confidence intervals show that the estimated contrasts are not sharply determined. An estimate that appears numerically higher in one group is not by itself evidence of a dependable difference. Equally, an interval spanning zero should not be converted into proof of equivalence.
The registry record highlights another statistical principle: outcomes can tell different parts of the story. Recurrence measures, survival and toxicity are related to the treatment comparison but are not interchangeable. The primary composite cannot identify which component drives its pattern, and secondary comparisons need cautious interpretation when multiplicity adjustment is not reported.
Finally, transparent reporting of missing-data handling, analysis populations, prespecified hypotheses and sample-size assumptions is essential for judging a trial result. Those details are not reported in the registry record summarized for these outcomes. A clear separation between posted group estimates, unadjusted recalculations and unreported analysis choices helps readers assess what the evidence can support without overstating certainty.
18. Limitations
- The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
- Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.
- Participant counts were reconstructed from posted percentages and arm sizes, so small rounding differences are possible.
Several limitations are specific to the reported record. The primary outcome description notes missing follow-up for 20 participants in Arm 1, 16 in Arm 2 and 17 in Arm 3, but does not describe how these observations entered the estimates. No sensitivity analysis for missing outcomes is reported. That leaves uncertainty about the robustness of the five-year percentages to alternative assumptions about participants without follow-up.
The registry provides a composite disease-free survival outcome but does not report its primary component results separately. It therefore cannot show whether any pattern was driven mainly by recurrence, a contralateral breast cancer, a second primary cancer, or death. The endpoint is reported at five years, and longer-term results are not present in the record.
The trial's original sample-size assumptions, planned primary statistical analysis, analysis-population definitions, interim procedures and multiplicity strategy are not reported in the registry record. The pairwise results discussed are unadjusted recalculations from posted summary statistics, and the registry lists no formal reported analyses. These recalculations may not capture features of the sponsor's analysis, such as adjustment or time-to-event methods.
The safety information also has limits: death counts are not reported, and the listed serious event terms are not presented with group-specific percentages in the summarized information. The registry does not provide details on event ascertainment or the full context needed to compare event burden. These reporting gaps restrict interpretation of the posted results; they are not evidence that the missing analyses or procedures were absent from the conduct of the trial.
19. Related Tutorials
20. Related Statistical Calculators
21. Sources
- ClinicalTrials.gov: Combination Chemotherapy in Treating Women Who Have Undergone Surgery for Node-Positive Breast Cancer — NCT00093795.
- Registry record last updated 2018-01-11; status last verified 2017-12.
- Results first posted 2017-12-12.
- Data retrieved from ClinicalTrials.gov on 2026-11-09.
- Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.
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22. Record Summary
The registry describes a completed randomized phase III parallel-group trial enrolling 4894 women with node-positive breast cancer after surgery. It compared TAC X 6 with AC X 4 then P X 4 and AC X 4 then PG X 4, without masking. The primary endpoint was five-year disease-free survival, reported as a percentage and defined to include recurrence, contralateral breast cancer, second primary cancer and death under the stated endpoint rules.
The posted primary estimates were 80.1%, 82.2% and 80.6% across the three groups. Unadjusted recalculated comparisons with TAC had confidence intervals that included zero. The record also lists recurrence, distant recurrence and toxicity outcomes, but formal analyses are not reported in the registry record. Missing follow-up is noted for each arm, while its handling and several important analysis and design details are not described.